Dynamics of Vibro-impact Systems with Randomly Changing Parameters

Chapter five is devoted to the study of the nonlinear dynamics of single-mass vibration-impact systems with small random changes in the recovery coefficient of speed and gap from those values at which a stable periodic regime exists in the deterministic case. For the first time, statistical characteristics have been determined in cases of delta-correlated and weekta-correlated changes in the coefficient of restoration and clearance; the values of parameters have been found at which small random deviations of the coefficient of restoration do not affect the single-impact mode of movement, as well as those parameters at which week-correlated changes have the same effect on the operation of the vibration-impact mechanism as with delta-correlated changes in the recovery coefficient of speed and clearance. A new concept of stochastic stability is introduced based on existing definitions. Based on the introduced definition, one can judge the degree of stochastic stability of the movement under consideration. Based on this, some practical recommendations have been made for selecting system parameters. The influence of random changes in the speed recovery coefficient on the value of the optimal impact speed has been studied. Digital modeling of the problem of the movement of a vibratory impactor with a random change in parameters has been carried out. The simulation results agree well with the theoretical ones with parameter deviations ranging from −0.05 to 0.05. An approximate value for the smallness of random changes has been found.